Abstract
We study representations of subgroups of the mapping class group M g of a surface of genus g≥2 arising from the actions of them on the first cohomology groups of the surface with local coefficient systems which are defined by nontrivial homomorphisms π 1(Σ g,∗)→ Z 2=Aut( Z) . As an application, in the case of g=2, we construct a function on M 2 which agrees with the Meyer function φ: M 2→ Q on the Torelli group J 2 .
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